- #1
Miles123K
- 57
- 2
- Homework Statement
- A string of tension T and linear density ##\rho## is driven at ##x=0## and two travelling wave in positive and negative x-direction had been created. Calculate the force and power applied to create the travelling wave.
I am studying chapter 8 of the book the physics of waves by Howard Georgi and I am quite confused. I read the entire chapter but I still don't quite get how to acquire the travelling wave mode of a system. Can someone check my solution to this problem but also explain how to systematically work out the "travelling wave mode" from conditions provided like this question?
- Relevant Equations
- ##\frac {\partial^2 \psi} {\partial t^2} = \frac T \rho \frac {\partial^2 \psi} {\partial x^2} ##
##F = - T \frac {\partial \psi} {\partial x}##
Again I am really confused, but I just put the traveling wave as:
##\psi(x,t) = Dcos(kx- \omega t)## for positive x
##\psi(x,t) = Dcos(kx+ \omega t)## for positive x
Then I simply differentiated and plugged in ##x=0##
##F(t) = - T D k sin(\omega t)##
and from this
## \langle P \rangle = T D^2 k \omega sin^2(\omega t)##
##\psi(x,t) = Dcos(kx- \omega t)## for positive x
##\psi(x,t) = Dcos(kx+ \omega t)## for positive x
Then I simply differentiated and plugged in ##x=0##
##F(t) = - T D k sin(\omega t)##
and from this
## \langle P \rangle = T D^2 k \omega sin^2(\omega t)##